Question

Calculate the Y values corresponding to the X values given below. Find the critical values for X for the given polynomial by finding the X values among those given where the first derivative, dv/dx- 0 and/orn X values where the second derivative, d-y/dx2-0. Be sure to find the sign (+ or-) of dv/dx and of d'y/dx2 at all X values. Using the first and second derivative tests with the information you have calculated, determine which X value(s) represent maximums (MAX), which minimums (MIN) and which inflection points (INF). Label the qualifying X value as such. Y 50 15X- 6.5X-2/3X 8.5-7.5-6.53.5 3.25 -3 dy/dx d'y/dx Label Point (MAX, MIN Use the nine X values and their Y values you found above (which include the critical values) to help neatly sketch the graph of this polynomial function over the range of X values given. Your sketch must be consistent with the tabled values above (which means, if you claim a certain X value is a maximum, then the graph of it should show this same value as a maximum. Similarly, if you claim an X value is an inflection point, then the graph of it should show it to be so. Write the first derivative (dv/dx) and the second derivative (d'y/dx-) used

Answer 1

Gve n polymomiaJ so+15%-6.SY느즐X y= 3 dy ) 7(27千15)-(274 3 maxinum value 65-65-2 347 =57.83 dx2

&s 3.3s 3 25 -3 2- y i -ts1-1| | -146-88 |_s? oy | _53.sy |-44.s2 |ー35. 5 | ร0 | ST.t? 3 6 636.12s dy IST 36 IS dl 2] 1ナ 13 2. Max/u TNI mioi pon (-7S-14ft) (-3.25,-44.12

200 100 max 578.1) So -50 min -1SO -200